# Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems

arXiv: https://arxiv.org/abs/2010.14685 · HTML: https://mlsanity.com/paper/2010.14685/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

## Built on by (most cited first, 30 of 45)

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- [Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximations](https://mlsanity.com/paper/2410.10174/) (2024)
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- [Do We Need an Encoder-Decoder to Model Dynamical Systems on Networks?](https://mlsanity.com/paper/2305.12185/) (2023)
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- [Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives](https://mlsanity.com/paper/2512.15997/) (2025)
- [Incorporating NODE with Pre-trained Neural Differential Operator for Learning Dynamics](https://mlsanity.com/paper/2106.04166/) (2021)
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- [Modeling chaotic Lorenz ODE System using Scientific Machine Learning](https://mlsanity.com/paper/2410.06452/) (2024)
- [3D-PDR Orion dataset and NeuralPDR: Neural Differential Equations for Photodissociation Regions](https://mlsanity.com/paper/2412.00758/) (2024)
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- [Understanding the role of autoencoders for stiff dynamical systems using information theory](https://mlsanity.com/paper/2503.06325/) (2025)
- [NeuralPDR: Neural Differential Equations as surrogate models for Photodissociation Regions](https://mlsanity.com/paper/2506.14270/) (2025)
- [Learning solutions of parameterized stiff ODEs using Gaussian processes](https://mlsanity.com/paper/2511.05990/) (2025)
- [NN-OpInf: an operator inference approach using structure-preserving composable neural networks](https://mlsanity.com/paper/2603.08488/) (2026)

## Abstract (arXiv)

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ordinary differential equations, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder-decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs with important benchmark problems from computational physics.